The mechanical energy, E, is defined as the sum of the kinetic energy, K, and the potential energy, U. In a system subjected to only conservative forces the mechanical energy is conserved, although it may be exchanged between potential and kinetic energies. You will investigate this conservation of energy in this lab, using the gravitational potential energy of a hanging mass to produce kinetic energy in the hanging mass and a cart. The basic setup you will use is like that of Experiment 5 (Force, Mass and Acceleration) where you attached a mass to a cart on the track and hung the mass over a pulley and allowed the gravitational pull on the hanging mass to pull the cart down the track. In this lab you will not need to measure the force or acceleration, so you will not be using the force sensor, and the motion sensor will be used to measure the speed directly. When the hanging mass is released, it and the cart will accelerate, converting the potential energy of the mass into kinetic energy of the cart and mass. (The potential energy can be calculated after measuring the height of the hanging mass.) When the mass hits the ground, the cart will stop accelerating and will move along the track at a constant speed (in the absence of friction). By measuring the speed of the cart after the string goes slack the kinetic energy of the system can be determined. From these measurements you can compare the mechanical energy of the system before and after the hanging mass fell to see if it is conserved.
Materials
Dynamics track with cart, cart mass block, motion sensor, pulley, hanging mass set, string, balance.
Procedure
· Setup the dynamics track with the motion sensor as you did in the Force, Mass & Acceleration lab. Setup your software so that the motion sensor shows you a graph of the speed of the cart. Setup your track so that the hanging mass is free to fall at least 80 cm.
· Use the carpenter’s level to level your track.
o Note: You will need to make sure the track does not move around on your table and get out of level as you do the experiment.
· Record the mass of your cart and the cart mass block.
· Hang a 50-g mass off the string over the pulley and raise it 10 – 20 cm off the floor. Note that you can measure the height of the mass using the scale on the dynamics track. Record the height of the mass, y.
o NOTE: Make sure that the mass is not swinging back and forth, as this will compromise your data.
· Start your data logging, release the cart, and let it accelerate along the track. Record the speed of the cart as the mass hits the ground. You should see a graph of increasing velocity that levels out and becomes almost constant, decreasing slightly. You want to record the maximum speed, which should occur as it levels out. (You may need to increase the sample rate to 20 Hz or larger in order to get a good graph.)
· Repeat this a total of 4 times and average the 4 speeds to obtain your value of v for this height of the mass.
· Use this data to calculate the initial and final values of the mechanical energy.
o Note: The m in Ug = mgy is the mass of the hanging mass.
o Note: The m in K = ˝mv2 is the mass of the cart plus the hanging mass (everything that is moving).
· Repeat your data runs to obtain a total of five different sets with values of y between 10 and 80 cm.
· Make a graph of K vs. Ug, assume a linear fit, and find the slope of your best fit line.
· Add the mass block to your cart to change the "m" in K = ˝mv2 and repeat your data runs to get five data sets with this new mass. Make a second graph of K vs. Ug, also finding the slope of the best fit line.
· From each graph calculate the % change in the mechanical energy. (If there is no change in the mechanical energy, the slope of each graph should be one--K = Ug. Therefore, the difference of your slope from 1 is the change in the mechanical energy.)
· When finished, put all your equipment up and clean off your lab table.
Questions
1. Allowing for a reasonable amount of experimental error, does your experiment support the conservation of mechanical energy?
2. What, if any, difference in your % change in mechanical energy do you see between the data sets with and without the mass block? Explain.
3. Describe an experimental procedure you could use to determine a numerical value for the amount of energy lost to friction in your setup.
4. What would be the effect on your experiment if the track were slightly tilted so the cart ran uphill? So the cart ran downhill?